Pressure activated safety valves have been incorporated into medical devices such as peripherally inserted central catheters (PICCs), ports, dialysis catheters and tunneled central catheters which provide long term access to the vascular system, etc. These valves generally include an elastic component that controls flow and/or pressure through the device to prevent flow therethrough when the device is not in use. The elastic component may be a slitted, flexible membrane extending across a lumen generally constructed so that, when subjected to a fluid pressure of at least a threshold magnitude, edges of the slit separate from one another to permit flow through the lumen. When the pressure applied to the membrane drops below the threshold level, the slit reseals to prevent leakage from or into the device. It is desirable to keep the flexible disk in place during high pressure and/or flow while maintaining the desired flow control characteristics of the membrane.